Simplify the following expression: $\dfrac{12r}{6r^2}$ You can assume $r \neq 0$.
Solution: $ \dfrac{12r}{6r^2} = \dfrac{12}{6} \cdot \dfrac{r}{r^2} $ To simplify $\frac{12}{6}$ , find the greatest common factor (GCD) of $12$ and $6$ $12 = 2 \cdot 2 \cdot 3$ $6 = 2 \cdot 3$ $ \mbox{GCD}(12, 6) = 2 \cdot 3 = 6 $ $ \dfrac{12}{6} \cdot \dfrac{r}{r^2} = \dfrac{6 \cdot 2}{6 \cdot 1} \cdot \dfrac{r}{r^2} $ $\phantom{ \dfrac{12}{6} \cdot \dfrac{1}{2}} = 2 \cdot \dfrac{r}{r^2} $ $ \dfrac{r}{r^2} = \dfrac{r}{r \cdot r} = \dfrac{1}{r} $ $ 2 \cdot \dfrac{1}{r} = \dfrac{2}{r} $